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Fairness-Enhancing Vehicle Rebalancing in the Ride-hailing Systemworkpreprint / 2023 / arXivOn Calibration and Out-of-domain Generalizationworkpreprint / 2022 / arXivFrom Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Modelsworkpreprint / 2026 / arXivMachine Learningtopic49008 works

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1,473-1,504 of 49,008

preprint2023arXiv

Fairness-Enhancing Vehicle Rebalancing in the Ride-hailing System

The rapid growth of the ride-hailing industry has revolutionized urban transportation worldwide. Despite its benefits, equity concerns arise as underserved communities face limited accessibility to affordable ride-hailing services. A key issue in this context is the vehicle rebalancing problem, where idle vehicles are moved to areas with anticipated demand. Without equitable approaches in demand forecasting and rebalancing strategies, these practices can further deepen existing inequities. In the realm of ride-hailing, three main facets of fairness are recognized: algorithmic fairness, fairness to drivers, and fairness to riders. This paper focuses on enhancing both algorithmic and rider fairness through a novel vehicle rebalancing method. We introduce an approach that combines a Socio-Aware Spatial-Temporal Graph Convolutional Network (SA-STGCN) for refined demand prediction and a fairness-integrated Matching-Integrated Vehicle Rebalancing (MIVR) model for subsequent vehicle rebalancing. Our methodology is designed to reduce prediction discrepancies and ensure equitable service provision across diverse regions. The effectiveness of our system is evaluated using simulations based on real-world ride-hailing data. The results suggest that our proposed method enhances both accuracy and fairness in forecasting ride-hailing demand, ultimately resulting in more equitable vehicle rebalancing in subsequent operations. Specifically, the algorithm developed in this study effectively reduces the standard deviation and average customer wait times by 6.48% and 0.49%, respectively. This achievement signifies a beneficial outcome for ride-hailing platforms, striking a balance between operational efficiency and fairness.

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preprint2022arXiv

On Calibration and Out-of-domain Generalization

Out-of-domain (OOD) generalization is a significant challenge for machine learning models. Many techniques have been proposed to overcome this challenge, often focused on learning models with certain invariance properties. In this work, we draw a link between OOD performance and model calibration, arguing that calibration across multiple domains can be viewed as a special case of an invariant representation leading to better OOD generalization. Specifically, we show that under certain conditions, models which achieve \emph{multi-domain calibration} are provably free of spurious correlations. This leads us to propose multi-domain calibration as a measurable and trainable surrogate for the OOD performance of a classifier. We therefore introduce methods that are easy to apply and allow practitioners to improve multi-domain calibration by training or modifying an existing model, leading to better performance on unseen domains. Using four datasets from the recently proposed WILDS OOD benchmark, as well as the Colored MNIST dataset, we demonstrate that training or tuning models so they are calibrated across multiple domains leads to significantly improved performance on unseen test domains. We believe this intriguing connection between calibration and OOD generalization is promising from both a practical and theoretical point of view.

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preprint2026arXiv

From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models

Physics-informed neural networks (PINNs) offer a mesh-free framework for solving partial differential equations (PDEs), yet training often suffers from gradient pathologies, spectral bias, and poor convergence, especially for problems with strong nonlinearity, sharp gradients, or multiscale features. We propose the Curriculum-Guided Gaussian Mixture Physics-Informed Neural Network (CGMPINN), which integrates Gaussian mixture modeling with dynamic curriculum learning. Specifically, a GMM is periodically fitted to the PDE residual distribution to quantify spatially varying learning difficulty. A smooth curriculum schedule progressively shifts training focus from easy to harder regions, while precision-based variance modulation suppresses unreliable clusters during early optimization. This dual curriculum is governed by a shared curriculum parameter and can be combined with self-adaptive loss balancing. We further establish theoretical guarantees, including sublinear convergence of the gradient norm for the induced time-varying loss, uniform equivalence between the curriculum-weighted and standard PDE losses, and a generalization bound with an explicit weighting-induced bias characterization. Experiments on six benchmark PDEs spanning elliptic, parabolic, hyperbolic, advection-dominated, and nonlinear reaction-diffusion types show that CGMPINN consistently achieves the lowest relative $L_2$ and maximum absolute errors among all compared methods, reducing relative $L_2$ error by up to 97.8\% over the standard PINN at comparable cost. Our code is publicly available at https://github.com/Mathematics-Yang/CGMPINN.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

COVID-19 Hospitalizations Forecasts Using Internet Search Data

As the COVID-19 spread over the globe and new variants of COVID-19 keep occurring, reliable real-time forecasts of COVID-19 hospitalizations are critical for public health decision on medical resources allocations such as ICU beds, ventilators, and personnel to prepare for the surge of COVID-19 pandemics. Inspired by the strong association between public search behavior and hospitalization admission, we extended previously-proposed influenza tracking model, ARGO (AutoRegression with GOogle search data), to predict future 2-week national and state-level COVID-19 new hospital admissions. Leveraging the COVID-19 related time series information and Google search data, our method is able to robustly capture new COVID-19 variants' surges, and self-correct at both national and state level. Based on our retrospective out-of-sample evaluation over 12-month comparison period, our method achieves on average 15\% error reduction over the best alternative models collected from COVID-19 forecast hub. Overall, we showed that our method is flexible, self-correcting, robust, accurate, and interpretable, making it a potentially powerful tool to assist health-care officials and decision making for the current and future infectious disease outbreak.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Mappings for Marginal Probabilities with Applications to Models in Statistical Physics

We present local mappings that relate the marginal probabilities of a global probability mass function represented by its primal normal factor graph to the corresponding marginal probabilities in its dual normal factor graph. The mapping is based on the Fourier transform of the local factors of the models. Details of the mapping are provided for the Ising model, where it is proved that the local extrema of the fixed points are attained at the phase transition of the two-dimensional nearest-neighbor Ising model. The results are further extended to the Potts model, to the clock model, and to Gaussian Markov random fields. By employing the mapping, we can transform simultaneously all the estimated marginal probabilities from the dual domain to the primal domain (and vice versa), which is advantageous if estimating the marginals can be carried out more efficiently in the dual domain. An example of particular significance is the ferromagnetic Ising model in a positive external magnetic field. For this model, there exists a rapidly mixing Markov chain (called the subgraphs--world process) to generate configurations in the dual normal factor graph of the model. Our numerical experiments illustrate that the proposed procedure can provide more accurate estimates of marginal probabilities of a global probability mass function in various settings.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Meta Discovery: Learning to Discover Novel Classes given Very Limited Data

In novel class discovery (NCD), we are given labeled data from seen classes and unlabeled data from unseen classes, and we train clustering models for the unseen classes. However, the implicit assumptions behind NCD are still unclear. In this paper, we demystify assumptions behind NCD and find that high-level semantic features should be shared among the seen and unseen classes. Based on this finding, NCD is theoretically solvable under certain assumptions and can be naturally linked to meta-learning that has exactly the same assumption as NCD. Thus, we can empirically solve the NCD problem by meta-learning algorithms after slight modifications. This meta-learning-based methodology significantly reduces the amount of unlabeled data needed for training and makes it more practical, as demonstrated in experiments. The use of very limited data is also justified by the application scenario of NCD: since it is unnatural to label only seen-class data, NCD is sampling instead of labeling in causality. Therefore, unseen-class data should be collected on the way of collecting seen-class data, which is why they are novel and first need to be clustered.

0 citations0 reviewsNo code linkedOpen access
preprint2011arXiv

High-dimensional covariance estimation based on Gaussian graphical models

Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\ell_1$-penalization methods. We propose and study the following method. We combine a multiple regression approach with ideas of thresholding and refitting: first we infer a sparse undirected graphical model structure via thresholding of each among many $\ell_1$-norm penalized regression functions; we then estimate the covariance matrix and its inverse using the maximum likelihood estimator. We show that under suitable conditions, this approach yields consistent estimation in terms of graphical structure and fast convergence rates with respect to the operator and Frobenius norm for the covariance matrix and its inverse. We also derive an explicit bound for the Kullback Leibler divergence.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

On the generalization of bayesian deep nets for multi-class classification

Generalization bounds which assess the difference between the true risk and the empirical risk have been studied extensively. However, to obtain bounds, current techniques use strict assumptions such as a uniformly bounded or a Lipschitz loss function. To avoid these assumptions, in this paper, we propose a new generalization bound for Bayesian deep nets by exploiting the contractivity of the Log-Sobolev inequalities. Using these inequalities adds an additional loss-gradient norm term to the generalization bound, which is intuitively a surrogate of the model complexity. Empirically, we analyze the affect of this loss-gradient norm term using different deep nets.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Scalable Bigraphical Lasso: Two-way Sparse Network Inference for Count Data

Classically, statistical datasets have a larger number of data points than features ($n > p$). The standard model of classical statistics caters for the case where data points are considered conditionally independent given the parameters. However, for $n\approx p$ or $p > n$ such models are poorly determined. Kalaitzis et al. (2013) introduced the Bigraphical Lasso, an estimator for sparse precision matrices based on the Cartesian product of graphs. Unfortunately, the original Bigraphical Lasso algorithm is not applicable in case of large p and n due to memory requirements. We exploit eigenvalue decomposition of the Cartesian product graph to present a more efficient version of the algorithm which reduces memory requirements from $O(n^2p^2)$ to $O(n^2 + p^2)$. Many datasets in different application fields, such as biology, medicine and social science, come with count data, for which Gaussian based models are not applicable. Our multi-way network inference approach can be used for discrete data. Our methodology accounts for the dependencies across both instances and features, reduces the computational complexity for high dimensional data and enables to deal with both discrete and continuous data. Numerical studies on both synthetic and real datasets are presented to showcase the performance of our method.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A survey on recently proposed activation functions for Deep Learning

Artificial neural networks (ANN), typically referred to as neural networks, are a class of Machine Learning algorithms and have achieved widespread success, having been inspired by the biological structure of the human brain. Neural networks are inherently powerful due to their ability to learn complex function approximations from data. This generalization ability has been able to impact multidisciplinary areas involving image recognition, speech recognition, natural language processing, and others. Activation functions are a crucial sub-component of neural networks. They define the output of a node in the network given a set of inputs. This survey discusses the main concepts of activation functions in neural networks, including; a brief introduction to deep neural networks, a summary of what are activation functions and how they are used in neural networks, their most common properties, the different types of activation functions, some of the challenges, limitations, and alternative solutions faced by activation functions, concluding with the final remarks.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

WarpLDA: a Cache Efficient O(1) Algorithm for Latent Dirichlet Allocation

Developing efficient and scalable algorithms for Latent Dirichlet Allocation (LDA) is of wide interest for many applications. Previous work has developed an O(1) Metropolis-Hastings sampling method for each token. However, the performance is far from being optimal due to random accesses to the parameter matrices and frequent cache misses. In this paper, we first carefully analyze the memory access efficiency of existing algorithms for LDA by the scope of random access, which is the size of the memory region in which random accesses fall, within a short period of time. We then develop WarpLDA, an LDA sampler which achieves both the best O(1) time complexity per token and the best O(K) scope of random access. Our empirical results in a wide range of testing conditions demonstrate that WarpLDA is consistently 5-15x faster than the state-of-the-art Metropolis-Hastings based LightLDA, and is comparable or faster than the sparsity aware F+LDA. With WarpLDA, users can learn up to one million topics from hundreds of millions of documents in a few hours, at an unprecedentedly throughput of 11G tokens per second.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Finding Valid Adjustments under Non-ignorability with Minimal DAG Knowledge

Treatment effect estimation from observational data is a fundamental problem in causal inference. There are two very different schools of thought that have tackled this problem. On one hand, Pearlian framework commonly assumes structural knowledge (provided by an expert) in form of directed acyclic graphs and provides graphical criteria such as back-door criterion to identify valid adjustment sets. On other hand, potential outcomes (PO) framework commonly assumes that all observed features satisfy ignorability (i.e., no hidden confounding), which in general is untestable. In prior works that attempted to bridge these frameworks, there is an observational criteria to identify an anchor variable and if a subset of covariates (not involving the anchor variable) passes a suitable conditional independence criteria, then that subset is a valid back-door. Our main result strengthens these prior results by showing that under a different expert-driven structural knowledge -- that one variable is a direct causal parent of treatment variable -- remarkably, testing for subsets (not involving the known parent variable) that are valid back-doors is equivalent to an invariance test. Importantly, we also cover the non-trivial case where entire set of observed features is not ignorable (generalizing the PO framework) without requiring knowledge of all parents of treatment variable. Our key technical idea involves generation of a synthetic sub-sampling (or environment) variable that is a function of the known parent variable. In addition to designing an invariance test, this sub-sampling variable allows us to leverage Invariant Risk Minimization, and thus, connects finding valid adjustments (in non-ignorable observational setting) to representation learning. We demonstrate effectiveness and tradeoffs of our approaches on a variety of synthetic data as well as real causal effect estimation benchmarks.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Dynamic Graph Structure Learning via Resistance Curvature Flow

Geometric Representation Learning (GRL) aims to approximate the non-Euclidean topology of high-dimensional data through discrete graph structures, grounded in the manifold hypothesis. However, traditional static graph construction methods based on Euclidean distance often fail to capture the intrinsic curvature characteristics of the data manifold. Although Ollivier-Ricci Curvature Flow (OCF) has proven to be a powerful tool for dynamic topological optimization, its core reliance on Optimal Transport (Wasserstein distance) leads to prohibitive computational complexity, severely limiting its application in large-scale datasets and deep learning frameworks. To break this bottleneck, this paper proposes a novel geometric evolution framework: Resistance Curvature Flow (RCF). Leveraging the concept of effective resistance from circuit physics, RCF transforms expensive curvature optimization into efficient matrix operations. This approach achieves over 100x computational acceleration while maintaining geometric optimization capabilities comparable to OCF. We provide an in-depth exploration of the theoretical foundations and dynamical principles of RCF, elucidating how it guides the redis

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preprint2022arXiv

Meta Sparse Principal Component Analysis

We study the meta-learning for support (i.e. the set of non-zero entries) recovery in high-dimensional Principal Component Analysis. We reduce the sufficient sample complexity in a novel task with the information that is learned from auxiliary tasks. We assume each task to be a different random Principal Component (PC) matrix with a possibly different support and that the support union of the PC matrices is small. We then pool the data from all the tasks to execute an improper estimation of a single PC matrix by maximising the $l_1$-regularised predictive covariance to establish that with high probability the true support union can be recovered provided a sufficient number of tasks $m$ and a sufficient number of samples $ O\left(\frac{\log(p)}{m}\right)$ for each task, for $p$-dimensional vectors. Then, for a novel task, we prove that the maximisation of the $l_1$-regularised predictive covariance with the additional constraint that the support is a subset of the estimated support union could reduce the sufficient sample complexity of successful support recovery to $O(\log |J|)$, where $J$ is the support union recovered from the auxiliary tasks. Typically, $|J|$ would be much less than $p$ for sparse matrices. Finally, we demonstrate the validity of our experiments through numerical simulations.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Stochastic Gradient Descent on Separable Data: Exact Convergence with a Fixed Learning Rate

Stochastic Gradient Descent (SGD) is a central tool in machine learning. We prove that SGD converges to zero loss, even with a fixed (non-vanishing) learning rate - in the special case of homogeneous linear classifiers with smooth monotone loss functions, optimized on linearly separable data. Previous works assumed either a vanishing learning rate, iterate averaging, or loss assumptions that do not hold for monotone loss functions used for classification, such as the logistic loss. We prove our result on a fixed dataset, both for sampling with or without replacement. Furthermore, for logistic loss (and similar exponentially-tailed losses), we prove that with SGD the weight vector converges in direction to the $L_2$ max margin vector as $O(1/\log(t))$ for almost all separable datasets, and the loss converges as $O(1/t)$ - similarly to gradient descent. Lastly, we examine the case of a fixed learning rate proportional to the minibatch size. We prove that in this case, the asymptotic convergence rate of SGD (with replacement) does not depend on the minibatch size in terms of epochs, if the support vectors span the data. These results may suggest an explanation to similar behaviors observed in deep networks, when trained with SGD.

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preprint2010arXiv

In All Likelihood, Deep Belief Is Not Enough

Statistical models of natural stimuli provide an important tool for researchers in the fields of machine learning and computational neuroscience. A canonical way to quantitatively assess and compare the performance of statistical models is given by the likelihood. One class of statistical models which has recently gained increasing popularity and has been applied to a variety of complex data are deep belief networks. Analyses of these models, however, have been typically limited to qualitative analyses based on samples due to the computationally intractable nature of the model likelihood. Motivated by these circumstances, the present article provides a consistent estimator for the likelihood that is both computationally tractable and simple to apply in practice. Using this estimator, a deep belief network which has been suggested for the modeling of natural image patches is quantitatively investigated and compared to other models of natural image patches. Contrary to earlier claims based on qualitative results, the results presented in this article provide evidence that the model under investigation is not a particularly good model for natural images

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preprint2024arXiv

A unified recipe for deriving (time-uniform) PAC-Bayes bounds

We present a unified framework for deriving PAC-Bayesian generalization bounds. Unlike most previous literature on this topic, our bounds are anytime-valid (i.e., time-uniform), meaning that they hold at all stopping times, not only for a fixed sample size. Our approach combines four tools in the following order: (a) nonnegative supermartingales or reverse submartingales, (b) the method of mixtures, (c) the Donsker-Varadhan formula (or other convex duality principles), and (d) Ville's inequality. Our main result is a PAC-Bayes theorem which holds for a wide class of discrete stochastic processes. We show how this result implies time-uniform versions of well-known classical PAC-Bayes bounds, such as those of Seeger, McAllester, Maurer, and Catoni, in addition to many recent bounds. We also present several novel bounds. Our framework also enables us to relax traditional assumptions; in particular, we consider nonstationary loss functions and non-i.i.d. data. In sum, we unify the derivation of past bounds and ease the search for future bounds: one may simply check if our supermartingale or submartingale conditions are met and, if so, be guaranteed a (time-uniform) PAC-Bayes bound.

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preprint2022arXiv

Approximate Latent Force Model Inference

Physically-inspired latent force models offer an interpretable alternative to purely data driven tools for inference in dynamical systems. They carry the structure of differential equations and the flexibility of Gaussian processes, yielding interpretable parameters and dynamics-imposed latent functions. However, the existing inference techniques associated with these models rely on the exact computation of posterior kernel terms which are seldom available in analytical form. Most applications relevant to practitioners, such as Hill equations or diffusion equations, are hence intractable. In this paper, we overcome these computational problems by proposing a variational solution to a general class of non-linear and parabolic partial differential equation latent force models. Further, we show that a neural operator approach can scale our model to thousands of instances, enabling fast, distributed computation. We demonstrate the efficacy and flexibility of our framework by achieving competitive performance on several tasks where the kernels are of varying degrees of tractability.

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preprint2022arXiv

Gaia: Graph Neural Network with Temporal Shift aware Attention for Gross Merchandise Value Forecast in E-commerce

E-commerce has gone a long way in empowering merchants through the internet. In order to store the goods efficiently and arrange the marketing resource properly, it is important for them to make the accurate gross merchandise value (GMV) prediction. However, it's nontrivial to make accurate prediction with the deficiency of digitized data. In this article, we present a solution to better forecast GMV inside Alipay app. Thanks to graph neural networks (GNN) which has great ability to correlate different entities to enrich information, we propose Gaia, a graph neural network (GNN) model with temporal shift aware attention. Gaia leverages the relevant e-seller' sales information and learn neighbor correlation based on temporal dependencies. By testing on Alipay's real dataset and comparing with other baselines, Gaia has shown the best performance. And Gaia is deployed in the simulated online environment, which also achieves great improvement compared with baselines.

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preprint2022arXiv

Stop&Hop: Early Classification of Irregular Time Series

Early classification algorithms help users react faster to their machine learning model's predictions. Early warning systems in hospitals, for example, let clinicians improve their patients' outcomes by accurately predicting infections. While early classification systems are advancing rapidly, a major gap remains: existing systems do not consider irregular time series, which have uneven and often-long gaps between their observations. Such series are notoriously pervasive in impactful domains like healthcare. We bridge this gap and study early classification of irregular time series, a new setting for early classifiers that opens doors to more real-world problems. Our solution, Stop&Hop, uses a continuous-time recurrent network to model ongoing irregular time series in real time, while an irregularity-aware halting policy, trained with reinforcement learning, predicts when to stop and classify the streaming series. By taking real-valued step sizes, the halting policy flexibly decides exactly when to stop ongoing series in real time. This way, Stop&Hop seamlessly integrates information contained in the timing of observations, a new and vital source for early classification in this setting, with the time series values to provide early classifications for irregular time series. Using four synthetic and three real-world datasets, we demonstrate that Stop&Hop consistently makes earlier and more-accurate predictions than state-of-the-art alternatives adapted to this new problem. Our code is publicly available at https://github.com/thartvigsen/StopAndHop.

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preprint2013arXiv

Bayesian Inference in Sparse Gaussian Graphical Models

One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity constraints on model structures. In this paper, we describe two new approaches to Bayesian inference of sparse structures of Gaussian graphical models (GGMs). One is based on a simple modification of the cutting-edge block Gibbs sampler for sparse GGMs, which results in significant computational gains in high dimensions. The other method is based on a specific construction of the Hamiltonian Monte Carlo sampler, which results in further significant improvements. We compare our fully Bayesian approaches with the popular regularisation-based graphical LASSO, and demonstrate significant advantages of the Bayesian treatment under the same computing costs. We apply the methods to a broad range of simulated data sets, and a real-life financial data set.

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preprint2022arXiv

Reward Uncertainty for Exploration in Preference-based Reinforcement Learning

Conveying complex objectives to reinforcement learning (RL) agents often requires meticulous reward engineering. Preference-based RL methods are able to learn a more flexible reward model based on human preferences by actively incorporating human feedback, i.e. teacher's preferences between two clips of behaviors. However, poor feedback-efficiency still remains a problem in current preference-based RL algorithms, as tailored human feedback is very expensive. To handle this issue, previous methods have mainly focused on improving query selection and policy initialization. At the same time, recent exploration methods have proven to be a recipe for improving sample-efficiency in RL. We present an exploration method specifically for preference-based RL algorithms. Our main idea is to design an intrinsic reward by measuring the novelty based on learned reward. Specifically, we utilize disagreement across ensemble of learned reward models. Our intuition is that disagreement in learned reward model reflects uncertainty in tailored human feedback and could be useful for exploration. Our experiments show that exploration bonus from uncertainty in learned reward improves both feedback- and sample-efficiency of preference-based RL algorithms on complex robot manipulation tasks from MetaWorld benchmarks, compared with other existing exploration methods that measure the novelty of state visitation.

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preprint2022arXiv

A Cramér Distance perspective on Quantile Regression based Distributional Reinforcement Learning

Distributional reinforcement learning (DRL) extends the value-based approach by approximating the full distribution over future returns instead of the mean only, providing a richer signal that leads to improved performances. Quantile Regression (QR) based methods like QR-DQN project arbitrary distributions into a parametric subset of staircase distributions by minimizing the 1-Wasserstein distance. However, due to biases in the gradients, the quantile regression loss is used instead for training, guaranteeing the same minimizer and enjoying unbiased gradients. Non-crossing constraints on the quantiles have been shown to improve the performance of QR-DQN for uncertainty-based exploration strategies. The contribution of this work is in the setting of fixed quantile levels and is twofold. First, we prove that the Cramér distance yields a projection that coincides with the 1-Wasserstein one and that, under non-crossing constraints, the squared Cramér and the quantile regression losses yield collinear gradients, shedding light on the connection between these important elements of DRL. Second, we propose a low complexity algorithm to compute the Cramér distance.

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preprint2022arXiv

GraphDCA -- a Framework for Node Distribution Comparison in Real and Synthetic Graphs

We argue that when comparing two graphs, the distribution of node structural features is more informative than global graph statistics which are often used in practice, especially to evaluate graph generative models. Thus, we present GraphDCA - a framework for evaluating similarity between graphs based on the alignment of their respective node representation sets. The sets are compared using a recently proposed method for comparing representation spaces, called Delaunay Component Analysis (DCA), which we extend to graph data. To evaluate our framework, we generate a benchmark dataset of graphs exhibiting different structural patterns and show, using three node structure feature extractors, that GraphDCA recognizes graphs with both similar and dissimilar local structure. We then apply our framework to evaluate three publicly available real-world graph datasets and demonstrate, using gradual edge perturbations, that GraphDCA satisfyingly captures gradually decreasing similarity, unlike global statistics. Finally, we use GraphDCA to evaluate two state-of-the-art graph generative models, NetGAN and CELL, and conclude that further improvements are needed for these models to adequately reproduce local structural features.

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preprint2020arXiv

Classification accuracy as a proxy for two sample testing

When data analysts train a classifier and check if its accuracy is significantly different from chance, they are implicitly performing a two-sample test. We investigate the statistical properties of this flexible approach in the high-dimensional setting. We prove two results that hold for all classifiers in any dimensions: if its true error remains $ε$-better than chance for some $ε>0$ as $d,n \to \infty$, then (a) the permutation-based test is consistent (has power approaching to one), (b) a computationally efficient test based on a Gaussian approximation of the null distribution is also consistent. To get a finer understanding of the rates of consistency, we study a specialized setting of distinguishing Gaussians with mean-difference $δ$ and common (known or unknown) covariance $Σ$, when $d/n \to c \in (0,\infty)$. We study variants of Fisher's linear discriminant analysis (LDA) such as "naive Bayes" in a nontrivial regime when $ε\to 0$ (the Bayes classifier has true accuracy approaching 1/2), and contrast their power with corresponding variants of Hotelling's test. Surprisingly, the expressions for their power match exactly in terms of $n,d,δ,Σ$, and the LDA appr

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preprint2015arXiv

Margins, Kernels and Non-linear Smoothed Perceptrons

We focus on the problem of finding a non-linear classification function that lies in a Reproducing Kernel Hilbert Space (RKHS) both from the primal point of view (finding a perfect separator when one exists) and the dual point of view (giving a certificate of non-existence), with special focus on generalizations of two classical schemes - the Perceptron (primal) and Von-Neumann (dual) algorithms. We cast our problem as one of maximizing the regularized normalized hard-margin ($ρ$) in an RKHS and %use the Representer Theorem to rephrase it in terms of a Mahalanobis dot-product/semi-norm associated with the kernel's (normalized and signed) Gram matrix. We derive an accelerated smoothed algorithm with a convergence rate of $\tfrac{\sqrt {\log n}}ρ$ given $n$ separable points, which is strikingly similar to the classical kernelized Perceptron algorithm whose rate is $\tfrac1{ρ^2}$. When no such classifier exists, we prove a version of Gordan's separation theorem for RKHSs, and give a reinterpretation of negative margins. This allows us to give guarantees for a primal-dual algorithm that halts in $\min\{\tfrac{\sqrt n}{|ρ|}, \tfrac{\sqrt n}ε\}$ iterations with a perfect separato

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preprint2020arXiv

RSO: A Gradient Free Sampling Based Approach For Training Deep Neural Networks

We propose RSO (random search optimization), a gradient free Markov Chain Monte Carlo search based approach for training deep neural networks. To this end, RSO adds a perturbation to a weight in a deep neural network and tests if it reduces the loss on a mini-batch. If this reduces the loss, the weight is updated, otherwise the existing weight is retained. Surprisingly, we find that repeating this process a few times for each weight is sufficient to train a deep neural network. The number of weight updates for RSO is an order of magnitude lesser when compared to backpropagation with SGD. RSO can make aggressive weight updates in each step as there is no concept of learning rate. The weight update step for individual layers is also not coupled with the magnitude of the loss. RSO is evaluated on classification tasks on MNIST and CIFAR-10 datasets with deep neural networks of 6 to 10 layers where it achieves an accuracy of 99.1% and 81.8% respectively. We also find that after updating the weights just 5 times, the algorithm obtains a classification accuracy of 98% on MNIST.

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preprint2026arXiv

Minimal-Intervention KV Retention via Set-Conditioned Diversity

KV-cache compression at small budgets is a crowded design space spanning cache representation, head-wise routing, compression cadence, decoding behavior, and within-budget scoring. We study seven mechanisms across these five families under matched mean cache on long-form mathematical reasoning (MATH-500~\cite{hendrycks2021math}) with two distilled-reasoning models (Qwen-7B and Llama-8B variants of DeepSeek-R1-Distill~\cite{deepseek2025r1}) at budgets $b \in \{64, 128\}$. All seven were rejected. We then propose $α$, a one-function modification to the TriAttention~\cite{mao2026triattention} retention scorer that replaces argmax-top-$k$ with greedy facility-location-inspired selection under a V-space redundancy penalty controlled by a single weight $λ$. A pre-registered protocol tunes $λ$ on a frozen development split and confirms on a disjoint held-out split; with $λ= 0.5$, $α$ clears Bonferroni on two of the four (model, budget) cells (Qwen $b{=}128$ and Llama $b{=}64$), no cell is significantly negative, and the pre-registered Branch~A triggers. The finding is asymmetric: a minimal scoring modification beat heavier structural redesigns in this regime, and the combined matched-memory, sympy-graded, held-out confirmation protocol is the evidence standard that made the asymmetry visible.

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preprint2026arXiv

Chebyshev Center-Based Direction Selection for Multi-Objective Optimization and Training PINNs

Physics-informed neural networks (PINNs) are a promising approach for solving partial differential equations (PDEs). Their training, however, is often difficult because multiple loss terms induced by PDE residuals and boundary or initial conditions must be optimized simultaneously. To address this difficulty, existing approaches often construct update directions by explicitly enforcing particular desirable properties, such as scale robustness and simultaneous descent. While effective in many cases, such property-by-property designs can make it unclear which conditions are essential, what geometric principle determines the selected update direction, and how different methods are structurally related. In this work, we formulate update-direction selection for PINN training as a Chebyshev-center problem in the dual cone. The proposed formulation selects a normalized direction that maximizes the minimum distance to the cone facets. The resulting formulation admits an efficient dual problem in a much lower-dimensional space and yields a convergence guarantee in the nonconvex setting. It also recovers the key desirable properties targeted by existing approaches without imposing them separately; rather, they follow from the single geometric criterion underlying the formulation. This makes the selected direction interpretable through a single geometric rule and provides a unified basis for systematically comparing related direction-selection methods. Experiments on several PINN benchmarks further demonstrate strong empirical performance of the proposed method.

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preprint2016arXiv

Theory reconstruction: a representation learning view on predicate invention

With this positional paper we present a representation learning view on predicate invention. The intention of this proposal is to bridge the relational and deep learning communities on the problem of predicate invention. We propose a theory reconstruction approach, a formalism that extends autoencoder approach to representation learning to the relational settings. Our intention is to start a discussion to define a unifying framework for predicate invention and theory revision.

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preprint2026arXiv

Learning Longitudinal Health Representations from EHR and Wearable Data

Foundation models trained on electronic health records show strong performance on many clinical prediction tasks but are limited by sparse and irregular documentation. Wearable devices provide dense continuous physiological signals but lack semantic grounding. Existing methods usually model these data sources separately or combine them through late fusion. We propose a multimodal foundation model that jointly represents electronic health records and wearable data as a continuous time latent process. The model uses modality specific encoders and a shared temporal backbone pretrained with self supervised and cross modal objectives. This design produces representations that are temporally coherent and clinically grounded. Across forecasting physiological and risk modeling tasks the model outperforms strong electronic health record only and wearable only baselines especially at long horizons and under missing data. These results show that joint electronic health record and wearable pretraining yields more faithful representations of longitudinal health.

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preprint2022arXiv

Understanding Value Decomposition Algorithms in Deep Cooperative Multi-Agent Reinforcement Learning

Value function decomposition is becoming a popular rule of thumb for scaling up multi-agent reinforcement learning (MARL) in cooperative games. For such a decomposition rule to hold, the assumption of the individual-global max (IGM) principle must be made; that is, the local maxima on the decomposed value function per every agent must amount to the global maximum on the joint value function. This principle, however, does not have to hold in general. As a result, the applicability of value decomposition algorithms is concealed and their corresponding convergence properties remain unknown. In this paper, we make the first effort to answer these questions. Specifically, we introduce the set of cooperative games in which the value decomposition methods find their validity, which is referred as decomposable games. In decomposable games, we theoretically prove that applying the multi-agent fitted Q-Iteration algorithm (MA-FQI) will lead to an optimal Q-function. In non-decomposable games, the estimated Q-function by MA-FQI can still converge to the optimum under the circumstance that the Q-function needs projecting into the decomposable function space at each iteration. In both settings, we consider value function representations by practical deep neural networks and derive their corresponding convergence rates. To summarize, our results, for the first time, offer theoretical insights for MARL practitioners in terms of when value decomposition algorithms converge and why they perform well.

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